Fast switch and spline scheme for accurate inversion of nonlinear functions: The new first choice solution to Kepler’s equation
作者：
Highlights：
• A universal algorithm for function inversion that does not require any initial guess.
• A novel theoretical analysis of the errors that agrees with the numerical results.
• Smaller errors than expected from general spline analysis, by a ∼10−22 factor for W ∈ [0; 10].
• For Kepler problem, its python code is ∼ 2000 times faster than Newton methods for large N.
• Method faster than Newton’s even for N ≥ 2 for Kepler problem with tolerance 10−6rad.
摘要
•A universal algorithm for function inversion that does not require any initial guess.•A novel theoretical analysis of the errors that agrees with the numerical results.•Smaller errors than expected from general spline analysis, by a ∼10−22 factor for W ∈ [0; 10].•For Kepler problem, its python code is ∼ 2000 times faster than Newton methods for large N.•Method faster than Newton’s even for N ≥ 2 for Kepler problem with tolerance 10−6rad.
论文关键词：Algorithm for inverse function,Cubic spline interpolation,Kepler equation for orbital motion,Astrodynamics,Newton-raphson iteration method,Lambert W function
论文评审过程：Received 30 December 2018, Revised 8 August 2019, Accepted 18 August 2019, Available online 27 August 2019, Version of Record 27 August 2019.
论文官网地址：https://doi.org/10.1016/j.amc.2019.124677
